Use the data to (a) find the coefficient of determination $r^2$ and interpret the result, and (b) find the standard error of estimates, and interpret the result. The table shows the combined city and highway fuel efficiency (in miles per gallon gasoline equivalent) and top speeds (in miles per hour) for nine hybrid and electric cars. The regression equation is $\hat{y}=-0.465 x+139.433$

$$\begin{matrix} \text{Fuel efficiency, x} & \text{114} & \text{95} & \text{120} & \text{105} & \text{107} & \text{116} & \text{118} & \text{68} & \text{84}\\ \text{Top speed, y} & \text{80} & \text{103} & \text{78} & \text{85} & \text{92} & \text{88} & \text{92} & \text{105} & \text{101}\\ \end{matrix}$$

Prove that any finite group has a finite exponent. Give an example of an infinite group with finite exponent. Does a finite group of exponent m always contain an element of order m?

Tami goes shopping and sees three kinds of shoes: flats, 2" heels, and 3" heels. The shoes come in two shades of beige (light and dark) and black. If each option has an equal chance of being selected, find the probabilities of the given events.

The shoes Tami buys have a 2" heel and are beige.

identify the claim and state $H_0$ and $H_a$.

Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. The table shows the weights (in pounds) for a sample of vacuum cleaners. The weights are classified according to vacuum cleaner type. At $\alpha=0.01$, can you conclude that at least one mean vacuum cleaner weight is different from the others?

$$\begin{matrix} \text{Bagged upright} & \text{21} & \text{22} & \text{23} & \text{21} & \text{17} & \text{19}\\ \text{Bagless upright} & \text{16} & \text{18} & \text{19} & \text{18} & \text{17} & \text{20}\\ \text{Bagged canister} & \text{26} & \text{24} & \text{23} & \text{25} & \text{27} & \text{21}\\ \end{matrix}$$

(a) identify the claim and state $H_0$ and $H_a$, (b) find the critical value and identify the rejection region, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Use the data, which list the hourly wages (in dollars) for randomly selected respiratory therapy technicians from three states. Assume the wages are normally distributed and that the samples are independent. Maine: 20.92, 25.37, 23.06, 15.64, 27.72, 24.90, 19.26, 23.46, 18.49. 21.76, 22.36. Oklahoma: 22.70. 19.95, 17.85, 16.76, 21.32, 18.96, 17.99, 28.35, 25.30, 21.93. Massachusetts: 25.43, 23.21, 30.81, 26.62, 31.42, 31.34, 34.58, 28.22, 27.25, 22.83, 27.45, 27.71. Are the mean hourly wages of respiratory therapist technicians the same for all three states? Use $\alpha=0.01$. Assume that the population variances are equal.

Model each application with a differential equation. All rates are assumed to be with respect to time. The voltage drop across an inductor is proportional to the rate at which the current is changing with respect to time.

(a) identify the claim and state

$$H _ { 0 }$$

and

$$H _ { a }$$

(b) find the critical value and identify the rejection region, (c) find the test statistic, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. If convenient, use technology. use the data. The data list the hourly wages (in dollars) for randomly selected respiratory therapy technicians from three states. Assume the wages are normally distributed and that the samples are independent.

$$\left. \begin{array} { c } { \text { Maine: } 23.66,28.69,26.07,17.69,31.35,28.16,21.78,26.53,20.91, } \\ { 24.61,25.28 } \end{array} \right.$$

$$\text { Oklahoma: } 21.76,19.13,17.11,16.07,20.44,18.18,17.25,27.18,24.26,21.03$$

$$\left. \begin{array} { c } { \text { Massachusetts: } 23.11,21.10,28.00,24.20,28.56,28.49,31.43,25.65,24.77, } \\ { 20.75,24.95,25.19 } \end{array} \right.$$

At

$$\alpha = 0.01$$

, is there enough evidence to conclude that the variance of the hourly wages for respiratory therapy technicians in Oklahoma is greater than the variance of the hourly wages for respiratory therapy technicians in Massachusetts?

Diagonalize the matrices if possible. The real eigenvalues are included below the matrix.

$$\begin{array}{c} {\left[\begin{array}{cc} 2 & 0 & -2 \\ 1 & 3 & 2 \\ 0 & 0 & 3 \end{array}\right]} \\ \lambda=2,3 \end{array}$$

The number of Medicare-certified home-health-care agencies (70% are freestanding, certified home-health-care agencies (70% are freestanding, been declining at the rate of $0.186 e^{-0.02 t}$ $0.186 e^{-0.02 t}$ thousand agencies/year between 1988 (t = 0) and 2002 (t = 14). The number of such agencies stood at 9.3 thousand in 1988. Find an expression giving the number of health-care agencies in year t.

Use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and postsecondary library science teachers in the United States for 12 years.

$$\begin{matrix} \text{Librarians, x} & \text{Library science teachers, y}\\ \text{49.1} & \text{56.6}\\ \text{50.9} & \text{57.6}\\ \text{52.9} & \text{59.7}\\ \text{54.7} & \text{61.6}\\ \text{55.7} & \text{64.3}\\ \text{56.4} & \text{67.0}\\ \text{57.0} & \text{70.0}\\ \text{57.2} & \text{70.8}\\ \text{57.6} & \text{73.3}\\ \text{58.1} & \text{72.4}\\ \text{58.9} & \text{73.0}\\ \text{59.9} & \text{72.3}\\ \end{matrix}$$

Find the coefficient of determination $r^2$ and interpret the result.

Use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and postsecondary library science teachers in the United States for 12 years.

$$\begin{matrix} \text{Librarians, x} & \text{Library science teachers, y}\\ \text{49.1} & \text{56.6}\\ \text{50.9} & \text{57.6}\\ \text{52.9} & \text{59.7}\\ \text{54.7} & \text{61.6}\\ \text{55.7} & \text{64.3}\\ \text{56.4} & \text{67.0}\\ \text{57.0} & \text{70.0}\\ \text{57.2} & \text{70.8}\\ \text{57.6} & \text{73.3}\\ \text{58.1} & \text{72.4}\\ \text{58.9} & \text{73.0}\\ \text{59.9} & \text{72.3}\\ \end{matrix}$$

Find the standard error of estimate $s_e$ and interpret the result.

Use the data in the table, which shows the average annual salaries (both in thousands of dollars) for librarians and postsecondary library science teachers in the United States for 12 years.

$$\begin{matrix} \text{Librarians, x} & \text{Library science teachers, y}\\ \text{49.1} & \text{56.6}\\ \text{50.9} & \text{57.6}\\ \text{52.9} & \text{59.7}\\ \text{54.7} & \text{61.6}\\ \text{55.7} & \text{64.3}\\ \text{56.4} & \text{67.0}\\ \text{57.0} & \text{70.0}\\ \text{57.2} & \text{70.8}\\ \text{57.6} & \text{73.3}\\ \text{58.1} & \text{72.4}\\ \text{58.9} & \text{73.0}\\ \text{59.9} & \text{72.3}\\ \end{matrix}$$

Calculate the correlation coefficient r and interpret the result.

Find the density of cX when X follows a gamma distribution. Show that only $\lambda$ is affected by such a transformation, which justifies calling $\lambda$ a scale parameter.

With your group, review "The Return" to identify elements of foreshadowing and situational irony in the story. Then, individually, complete the charts to understand how foreshadowing sets up expectations that affect situational irony. Finally, gauge the impact of situational irony on what the story says about homecomings.

$$\begin{array}{|l|l|l|}\hline & \text{FORESHADOWING IN "THE RETURN"} & \\\hline \text{STORY CLUES} & \text{QUESTIONS RAISED} & \text{WHAT THE CLUES SUGGEST}\\ \hline \\ \hline \\ \hline \\ \hline & \text{SITUATIONAL IRONY IN "THE RETURN"} & \\ \hline \text{EXPECTATIONS} & \text{WHAT ACTUALLY HAPPENS} & \text{CONNECTION TO THE STORY'S MEANING}\\ \hline \\ \hline \\ \hline \\ \hline \end{array}$$